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An application of abstract interpretation of logic programs: Occur check reduction [chapter]

Harald Søndergaard
1986 Lecture Notes in Computer Science  
The framework, however, differs in that we systematically apply the abstract interpretation princlple to loglc programs.  ...  The occur check in Robinson unification is superfluous in most unifications that take place in practice.  ...  Abstract Interpretation of Logic Programs The principle of abstract interpretation is rather well established in the case of imperative languages (Cousot 1977) .  ... 
doi:10.1007/3-540-16442-1_25 fatcat:b3mmv5xuqneyram4m4c2o2utc4

Programmed Strategies for Program Verification

Richard B. Kieburtz
2007 Electronical Notes in Theoretical Computer Science  
In Programatica, predicate definitions and property assertions written in P-logic, a programming logic for Haskell, can be embedded in the text of a Haskell program module.  ...  Properties refine the type system of Haskell but cannot be verified by type-checking alone; a more powerful logical verifier is needed.  ...  If reduction is suspended under abstractions, then the form reached is called a head normal form and if it is, in addition, suspended in the rand term of an application, exhaustive reduction stops at a  ... 
doi:10.1016/j.entcs.2007.02.045 fatcat:3gnit7ab3zd4hilkj7h2ahsjmu

Model checking programs

W. Visser, K. Havelund, G. Brat, Seungjoon Park
2000 Proceedings ASE 2000. Fifteenth IEEE International Conference on Automated Software Engineering  
JPF has been applied to a real-time avionics operating system developed at Honeywell, illustrating an intricate error, and to a model of a spacecraft controller, illustrating the combination of abstraction  ...  Part of this work has consisted of building a new Java Virtual Machine that interprets Java bytecode.  ...  Specifically, we are investigating the use of abstract interpretation, static analysis and runtime analysis to allow more efficient model checking of Java programs.  ... 
doi:10.1109/ase.2000.873645 dblp:conf/kbse/VisserHBP00 fatcat:c3kuoib74fexxjt4tjdsfiw54i

Reduction Strategies for Declarative Programming

Michael Hanus
2001 Electronical Notes in Theoretical Computer Science  
This paper surveys reduction or evaluation strategies for functional and functional logic programs.  ...  On the other hand, they should also support the programmers to write programs in a declarative way ignoring the influence of the evaluation strategy to the success of a computation as good as possible.  ...  Thus, an equational reading of each program rule should be supported so that one can check the validity of the program by checking its individual parts.  ... 
doi:10.1016/s1571-0661(04)00273-7 fatcat:jtcnfes5ireuxlctdpm6nxkehm

A bottom-up polymorphic type inference in logic programming

Roberto Barbuti, Roberto Giacobazzi
1992 Science of Computer Programming  
We present a type inference system for Horn clause logic programs, based on a bottom-up abstract interpretation technique.  ...  Through the definition of suitable abstract operators, we obtain an abstract immediate consequence operator map associated with the program to analyze.  ...  Since the application of reduction rules needs unification, we use a Prolog program P' to perform reductions.  ... 
doi:10.1016/0167-6423(92)90038-d fatcat:azxbd5i5u5cyfd2i3ylnsvgr7i

Verified programming in Guru

Aaron Stump, Morgan Deters, Adam Petcher, Todd Schiller, Timothy Simpson
2008 Proceedings of the 3rd workshop on Programming languages meets program verification - PLPV '09  
Operational Type Theory (OpTT) is a type theory allowing possibly diverging programs while retaining decidability of type checking and a consistent logic.  ...  This paper gives an introduction to verified programming in GURU.  ...  In LF encoding methodology, proof checking in an object logic is reduced to type checking in LF.  ... 
doi:10.1145/1481848.1481856 dblp:conf/plpv/StumpDPSS09 fatcat:rejqclc2qnhvjhwvrdqxqrsvme

Types and trace effects of higher order programs

CHRISTIAN SKALKA, SCOTT SMITH, DAVID VAN HORN
2007 Journal of functional programming  
The properties verified are based on the ordered sequence of events that occur during program execution, so called event traces.  ...  This paper shows how type effect systems can be combined with model-checking techniques to produce powerful, automatically verifiable program logics for higher order programs.  ...  Our type-based approach is defined directly at the language level, and type inference provides an explicit, scalable mechanism for extracting an abstract program interpretation, which is applicable to  ... 
doi:10.1017/s0956796807006466 fatcat:but7xa5q3zcq3fxxx3enqbct5i

Abstract interpretation and application to logic programs

Patrick Cousot, Radhia Cousot
1992 The Journal of Logic Programming  
Applications of Abstract Interpretation of Logic Programs [154] argue that abstract interpretation of logic programs can be quite precise, yet not overly expensive and therefore has reached the stage of  ...  For example the query q would succeed in the following logic program: when executed without occur-check.  ... 
doi:10.1016/0743-1066(92)90030-7 fatcat:xrgsohne6nebhchwcsk7khucma

Resolution and type theory

Leen Helmink
1991 Science of Computer Programming  
., Resolution and type theory, Science of Computer Programming 17 (1991) 119-138. In this paper, an inference mechanism is proposed for proof construction in Constructive Type Theory.  ...  This rests on a mechanism that provides a simple clausal interpretation for the assumptions in a context. The method is not complete, due to the expressive power of type theory.  ...  A previous version of this article appeared as [20] .  ... 
doi:10.1016/0167-6423(91)90038-y fatcat:7m4ktl6y7rdqxk6vyqojuygd6y

Program Logics for Homogeneous Meta-programming [chapter]

Martin Berger, Laurence Tratt
2010 Lecture Notes in Computer Science  
We show the applicability of our approach by reasoning about example meta-programs from the literature.  ...  This paper provides the first program logics for homogeneous metaprogramming -using a variant of MiniML e by Davies and Pfenning as underlying meta-programming language.  ...  A logical full abstraction result [13] is an important step towards integrating logics for meta-programming with logics for the produced meta-programs.  ... 
doi:10.1007/978-3-642-17511-4_5 fatcat:enz6xvuksvhtlkum47jmefagom

A Meta-Programming Approach to Realizing Dependently Typed Logic Programming [article]

Zachary Snow and David Baelde and Gopalan Nadathur
2010 arXiv   pre-print
Such calculi can also be given a logic programming interpretation: the Twelf system is based on such an interpretation of LF.  ...  We consider here whether a conventional logic programming language can provide the benefits of a Twelf-like system for encoding type and proof-and-formula dependencies.  ...  Opinions, findings, and conclusions or recommendations expressed in this papers are those of the authors and do not necessarily reflect the views of the National Science Foundation.  ... 
arXiv:1005.4379v1 fatcat:z3us722me5dlnhsm5k4ijz3l4e

Logic programming with equations

Maarten H. Van Emden, Keitaro Yukawa
1987 The Journal of Logic Programming  
We investigate how equational rewriting, which we assume is an adequate model for functional programming, can be performed within the context of logic programming.  ...  In the interpretational approach we use as logic program the equations themselves, but replace the standard axioms of equality by suitably chosen logical consequences having the property that the PROLOG  ...  If an SLD-refutation procedure uses (Eq'4) first whenever one of the arguments of f is noncanonical, it gives the effect of the innermost reduction (also called the applicative order reduction).  ... 
doi:10.1016/0743-1066(87)90006-9 fatcat:phjfsgt77fch7ggaiqpagtwxmu

Inductive Beluga: Programming Proofs [chapter]

Brigitte Pientka, Andrew Cave
2015 Lecture Notes in Computer Science  
are well-founded and correspond to inductive proofs 4) we describe an interactive program development environment.  ...  To demonstrate beluga's strength and illustrate these new features we develop a weak normalization proof using logical relations.  ...  This is an essential step to check that the given recursive program constitutes an inductive proof. Interactive Proof Development Similar to other interactive development modes (e.g.  ... 
doi:10.1007/978-3-319-21401-6_18 fatcat:jrmbnek7bfbordpjvnwn7r7q6i

Answer Set Programming [chapter]

Piero Bonatti, Francesco Calimeri, Nicola Leone, Francesco Ricca
2010 Lecture Notes in Computer Science  
The Italian logic programming community has been very active in this area, some ASP results achieved in Italy are widely recognized as milestones on the road to the current state of the art.  ...  Answer Set Programming (ASP), referred to also as Disjunctive Logic Programming under the stable model semantics (DLP), is a powerful formalism for Knowledge Representation and Reasoning.  ...  An ASP program (also called Disjunctive Logic Program or DLP program) P is a finite set of rules.  ... 
doi:10.1007/978-3-642-14309-0_8 fatcat:m7vjxp43qfbgjpujf7ozr72x5q

Integrating Logic Programming and Production Systems in Abductive Logic Programming Agents [chapter]

Robert Kowalski, Fariba Sadri
2009 Lecture Notes in Computer Science  
In this paper we argue the case for integrating the distinctive functionalities of logic programs and production systems within an abductive logic programming agent framework.  ...  In this framework, logic programs function as an agent's beliefs and production rules function as the agent's goals.  ...  logic-based semantics with an operational semantics that operates with the current state of a destructively changing database.  ... 
doi:10.1007/978-3-642-05082-4_1 fatcat:btdhdr5b5rg5favxoixqz2e534
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